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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Recording of various grating amplitude shapes during four-wave mixing in strong-response PRC

S. Bugaychuk, A. I. Khyzniak, A. G. Kutana

Published Sep 23, 1998• 0 citations
Publisher

Abstract

The amplitude of the transmission dynamic grating recorded due to the backward four-wave mixing (BFWM) in the non-local response photorefractive crystal is investigated theoretical. The grating's amplitude distribution is described as a motionless soliton. Both the soliton localization degree and its location can be control by varying of input intensity's ratio or/and input waves' phase differences. When waves' phase differences equal to 0 of (pi) the steady stage double-phase-conjugation mirror is formed. The BFWM dynamic is described by sin-Gordan-like equation.

DOI
10.1117/12.323713

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The amplitude of the transmission dynamic grating recorded due to the backward four-wave mixing (BFWM) in the non-local response photorefractive crystal is investigated theoretical. The grating's amplitude distribution is described as a motionless soliton. Both the soliton localization degree and its location can be control by varying of input intensity's ratio or/and input waves' phase differences. When waves' phase differences equal to 0 of (pi) the steady stage double-phase-conjugation mirror is formed. The BFWM dynamic is described by sin-Gordan-like equation.
Recording of localized transmission gratings by four-wave mixing in non-local photorefractive media with strong response is considered. The input conditions to record dynamic gratings with a stable grating amplitude distribution as well as grating amplitude oscillations are defined. They are determined both by intensities and by a phase difference of input waves. The influence of fluctuations of wave phases on stability of the recorded gratings is considered. Methods of optical control of both the grating amplitude localization degree and the grating amplitude location are defined.
The structure of the transmission dynamic grating, that is formed during four-wave mixing in photorefractive medium with non-local response, was theoretical investigated. It was obtained the steady state solution for the common case of four input waves with its arbitrary phases. It is shown, that the structure of the dynamic grating is differed by its grating amplitude distribution, which described by the `soliton'-like function. It was determined the manner, how the grating amplitude distribution is depending on parameters of input coupling beams: intensities ratio and phases of waves. Input variation of waves parameters brings two phenomena: (1) changing of the grating half-wide; (2) changing of the grating amplitude maximum position. It was shown what in case of four input wave it is possible to record any shape of the grating amplitude distribution by varying input waves intensities or phases.
The structure and dynamics of the four-wave mixing transmission grating in a photorefractive crystal were investigated. The steady-state grating’s amplitude distribution looks like a motionless soliton. When the value of coupling strength is more than 2, there are three solutions for the steady-state grating: two stable and one unstable. The dynamics of all these gratings are described by the sine-Gordon equation. The four-wave mixing grating’s structure and location in space are determined by the input beams’ ratio, phase difference, or both.
The effect of biasing illumination on the degenerate four-wave mixing (DFWM) in absorbing photorefractive (PR) media has been investigated. The input beams are considered to be spatially uniform. The analysis has been made both for transmission and reflection geometry. Considering pump beam depletion and the slowly varying amplitude approximation, nonlinear coupled wave equations are obtained and have been solved numerically by a shooting method. The effect of different parameters such as input beam intensities ratio, thickness of the interacting medium on the phase conjugate reflectively (PCR) has been investigated. It has been observed that PCR can be controlled to a large extent by controlling the biasing intensity.
Phase conjugate reflectivity of the photorefractive four-wave mixing system is usually quite unstable and it is serious issue for practical use of these systems. The cause of this instability is mainly combination of the fluctuation of the phases of input signal and pump beams and the slow response time of the photorefractive crystal. When all input beams in the four-wave mixing system are mutually coherent and the phases of the input beams are not stable, four kinds of gratings are compete each other and the phase conjugate output becomes quite unstable. To avoid this problem, we can make one of the pump incoherent to the signal and another pump1. The phase conjugate output is, however, still unstable due to the rewriting of the grating caused by the fluctuation of the phase of the input beams. In this paper, we report our feedback system to stabilize the power of the phase conjugate output from the four-wave mixing system by controlling the phase of the signal beam. In this system, we detect the phase difference between signal and forward pump beam with lock-in amplifier and control the phase of the signal with a piezoelectric mirror to stabilize the phase difference.